The Brachistochrone problem is famous in physics. It attempts to find the shape of the ramp that will allow a marble to roll under gravity from point A to point B in the least time. It was solved by Newton and Bernoulli and found to be a cycloid. This shape is a tradeoff between the considerations of minimizing the total path length, while still allowing the marble to be low, where it moves faster. In fact, sometimes the optimal track actually dips below point B, but still ends up being faster because of the increase in speed.

The Latin phrase on the front of the model, tanquam ex ungue leonem "we know the lion by his claw" was said by Johann Bernoulli in 1697 about how he knew Isaac Newton was the author of an anonymously submitted solution to his challenge.

References:
https://en.wikipedia.org/wiki/Brachistochrone_curve
http://mathworld.wolfram.com/BrachistochroneProblem.html